Parallelogram Pile

I made this because of a beautiful image from @tilman: [url]http://geometrydaily.tumblr.com/post/45757253199/399-ashes-of-the-triangle-a-new-minimal[/url]
A lot of terrific geometry here around similarity and parallelogram properties. And the big question: how do you construct these parallelograms so they all line up to make a triangle?